Archie's Law

Description

In petrophysics, Archie’s law relates the in-situ electrical conductivity of a sedimentary rock to its porosity and brine saturation as shown here.

It is a purely empirical law attempting to describe ion flow (mostly sodium and chloride) in clean, consolidated sands, with varying intergranular porosity. Electrical conduction is assumed not to be present within the rock grains or in fluids other than water.

Archie’s law is named after Gus Archie (1907–1978) who developed this empirical quantitative relationship between porosity, electrical conductivity, and brine saturation of rocks. Archie’s law laid the foundation for modern well log interpretation as it relates borehole electrical conductivity measurements to hydrocarbon saturations (which, for fluid saturated rock, equals 1-S_w).

Related formulas

Variables

Ctelectrical conductivity of the fluid saturated rock (S/m)
atortuosity factor (dimensionless)
Cwelectrical conductivity of the brine (S/m)
ϕporosity (dimensionless)
mcementation exponent of the rock (usually in the range 1.8–2.0 for sandstones) (dimensionless)
Swbrine saturation (dimensionless)
nsaturation exponent (usually close to 2) (dimensionless)